The 24-year-old hitman, who is on loan from West Brom, scored the only goal of the game with a well-timed header past Nicky Weaver in the 63rd minute to lift Palace out of the bottom three and pile the pressure on Addicks boss Alan Pardew.
Palace started brightly and Nicky Bailey was forced to head Paul Ifill's curling effort from the edge of the box over his own bar in the third minute.
The biggest cheer of the opening 25 minutes came when the returning Mark Hudson, who swapped Palace for Charlton in the summer, played a wayward pass that ballooned out for a throw.
Victor Moses shaved Weaver's left-hand post with a low curling effort from 25 yards in the 29th minute, before Ifill squandered a superb opportunity when his angled drive was turned away by Weaver.
And from the resulting corner, Beattie hit the bar with a deft header as Palace began to turn the screw.
Hameur Bouazza mustered up Charlton's best and only real chance of the opening period in the 38th minute when his angled drive from 14 yards was easily palmed away by Julian Speroni.
Ifill should have given Palace the lead a minute into the second period after Nick Carle's effort that was saved by Weaver rolled into his path.
However from seven yards out and the goal gaping, the former Millwall man somehow managed to miscue his effort wide.
The winger then missed another golden opportunity two minutes later but, with time and space, Ifill sent his neat turn and shot from close range just wide.
But Palace were finally rewarded for their dominance in the 63rd minute when Ben Watson's deep cross was headed home by Beattie.
Jose Fonte then crashed a header onto the bar from an out-swinging Watson corner in the 71st minute as the home side looked to put the game to bed.
Luke Varney nearly made Palace pay for their wastefulness but the striker failed to pounce on a moment of confusion from Speroni and Portuguese defender Fonte in the 76th minute as Neil Warnock's men held on for only their second league win of the season.